Metaheuristics for Robotics [Hardcover]

This book is dedicated to the application of metaheuristic optimization in trajectory generation and control issues in robotics. In this area, as in other fields of application, the algorithmic tools addressed do not require a comprehensive list of eligible solutions to effectively solve an optimization problem. This book investigates how, by reformulating the problems to be solved, it is possible to obtain results by means of metaheuristics.

Through concrete examples and case studies ? particularly related to robotics ? this book outlines the essentials of what is needed to reformulate control laws into concrete optimization data.

The resolution approaches implemented ? as well as the results obtained ? are described in detail, in order to give, as much as possible, an idea of metaheuristics and their performance within the context of their application to robotics.

Preface ix

Introduction xiii

Chapter 1. Optimization: Theoretical Foundations and Methods 1

1.1. The formalization of an optimization problem 1

1.2. Constrained optimization methods 5

1.2.1. The method of Lagrange multipliers 9

1.2.2. Method of the quadratic penalization 11

1.2.3. Methods of interior penalties 12

1.2.4. Methods of exterior penalties 13

1.2.5. Augmented Lagrangian method 14

1.3. Classification of optimization methods 15

1.3.1. Deterministic methods 16

1.3.2. Stochastic methods 18

1.4. Conclusion 21

1.5. Bibliography 22

Chapter 2. Metaheuristics for Robotics 27

2.1. Introduction 27

2.2. Metaheuristics for trajectory planning problems 28